Multi-dimensional modulation codes for fading channel

Some new codes are presented which have good performance on Rician fading channel with small decoding complexities. A new M-way partition chain is proposed for the L x MPSK (L less than or equal to M) signal set which maximizes the intra-set distance of each subset at each partition level. Based on this partition chain, a class of asymptotical optimum codes was found. For M = 4, these codes have both large symbol distances and product distances. Multi-level coding scheme allows to construct a code by hand such that the code meets some desired parameters, e.g., symbol distance, product distance, etc. In design of a multi-level code, all factors were considered which affect the performance and complexity of the code, such as, the decoding scheme, decoding complexity, and performance under the decoding scheme, e.g., if the multi-stage decoding scheme is used, the performance degradation due to the suboptimum decoding is taken into consideration. The performance for most of the presented codes was simulated on Rayleigh fading channel, and the results show that these codes have good performance with small decoding complexities.